For g(x)= 1/5x^2+3x, find g'(1) a. -1/4 b. 1/4 c. -7/4 d. -4/7 e. 7/4

mr Goodwill [35]

9514 1404 393

Answer:

1 triangle: 2 m²
2 triangles: 4 m²
large rectangle: 32 m²
small rectangle: 3 m²
total area: 39 m²
cost of tile: $487.50

Step-by-step explanation:

You will run across many examples of poorly edited curriculum materials. This is one of them. We presume that every instance of "inches" should be an instance of "meters". The difference between in and m is not always obvious in a diagram, and m apparently got misinterpreted here.

__

The area of a triangle is given by the formula ...

A = 1/2bh

where b is the base and h is the height perpendicular to the base.

The triangles in this figure have a base of 4 m, and a height of 1 m. Using this formula, we find the area of 1 triangle to be ...

A = 1/2(4 m)(1 m) = 2 square meters . . . . area of 1 triangle

__

The triangles are the same size, so the area of both together is ...

2(2 m²) = 4 square meters . . . . area of both triangles together

__

The large rectangle is 8 m long and 4 m high. Its area is given by the formula ...

A = LW

where the length is L and the width is W. Using this formula, we find the area of the large rectangle to be ...

A = (8 m)(4 m) = 32 m² . . . . area of large rectangle

__

The small rectangle has a length of 3 m and a width of 1 m. Its area is ...

A = (3 m)(1 m) = 3 m² . . . . area of small rectangle

__

The total area is the sum of the areas of the pieces:

total area = 2 triangles + large rectangle + small rectangle

total area = 4 m² + 32 m² + 3 m² = 39 square meters

_____

At $12.50 per square meter, the cost of covering the patio is ...

($12.50/m²)(39 m²) = $487.50 . . . . cost of tile

5 0

3 years ago

What is the function? F(x)=2x^2-3x+1

olasank [31]

Answer:

To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.

Step-by-step explanation:

As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.

To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:

dfdx=4x−3

f(b)−f(a)b−a=f'(c)

f(x)x=0=1

f(x)x=2=3

Hence:

3−12=4c−3

and c=1.

4 0

3 years ago

Read 2 more answers

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writin

Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

Let $\mu$ = true average writing lifetime under controlled conditions

So, Null Hypothesis, $H_0$ : $\mu \geq$ 10 hr {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, $H_A$ : $\mu$ < 10 hr {means that the true average writing lifetime under controlled conditions is less than 10 hr}

The test statistics that is used here is one-sample t test statistics;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean

s = sample standard deviation

n = sample size of pens = 18

n - 1 = degree of freedom = 18 -1 = 17

Now, the decision rule based on the critical value of t is given by;

If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then we will reject our null hypothesis as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0

3 years ago

Use the line of best fit to determine how many popsicles would be sold when the temperature is 100°.

SpyIntel [72]

Answer:

A!

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Can someone plz help me with this plzz

vesna_86 [32]

Answer:

hi how are you wanna be friend

Step-by-step explanation:

6 0

2 years ago