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2 years ago

Find the value of n such that b^2 + 16b + n is a perfect square trinomial

Mathematics

1 answer:

MariettaO [177]2 years ago

7 0

Answer:

Step-by-step explanation:

To complete the square

add ( half the coefficient of the b- term )² to b² + 16b

b² + 2(8)b + 8²

= b² + 16b + 64 = (b + 8)²

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Indicate whether the following statement is true or false: A linear function eventually exceeds a quadratic function with a posi

MA_775_DIABLO [31]

Answer:

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Step-by-step explanation:

idk tbh

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3 years ago

Will mark brainliest to best answer, i need it asap!!!!!!!!!!!!!

Paha777 [63]

Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

A cone-shaped pile of sawdust has a base diameter of 38 feet, and is 14 feet tall. Find the volume of the pile

Romashka-Z-Leto [24]

Answer:

Given: Diameter of cone = 38 feet and height of cone = 14 feet.

Volume of cone V with radius r is one-third the area of the base B times the height h.

i,e $V = \frac{1}{3} B \cdot h$ = $\frac{1}{3} \pi r^2h$ ......[1]

,where B = $\pi r^2$

First find the radius(r);

Using Diameter(D) = 2r

38 =2r

Divide both side by 2 we get;

$\frac{38}{2} =\frac{2r}{2}$

Simplify:

19 = r

or r =19 feet

Now, substitute the value of r = 19 feet and h = 14 feet in [1] [ Use value of $\pi = \frac{22}{7}$ ]

then, we have:

$V = \frac{1}{3} \pi r^2h = \frac{1}{3} \cdot \frac{22}{7} \cdot (19)^2 \cdot (14)$

V = $=\frac{1}{3}\cdot 22 \cdot 19 \cdot 19 \cdot 2 = \frac{22 \cdot 19 \cdot 19 \cdot 2}{3}$

V = $\frac{15884}{3} =5,294.66667$ ≈ 5,294.67 cubic feet.

therefore, the volume of pile is; ≈ 5,294.67 cubic feet.

4 0

3 years ago

Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

8 0

2 years ago

Nationwide, it is estimated that 40% of service stations have gas tanks that leak to some extent. A new program in California is

fredd [130]

Answer:

Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .

Step-by-step explanation:

The sample proportion is p2= 7/27= 0.259

and q2= 0.74

The sample size = n= 27

The population proportion = p1= 0.4

q1= 0.6

We formulate the null and alternate hypotheses that the new program is effective

H0: p2> p1 vs Ha: p2 ≤ p1

The test statistic is

z= p2- p1/√ p1q1/n

z= 0.259-0.4/ √0.4*0.6/27

z= -0.141/0.09428

z= -1.496

The significance level ∝ is 0.05

The critical region for one tailed test is z ≤ ± 1.645

Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .

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3 years ago