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A pyramid with a square base is cut by a plane that is parallel to its base and is 2 units from the base. The surface area of th

icang [17]

Answer:

6.83 units

Step-by-step explanation:

Let the height of the original pyramid be represented by h. Then the cut off top has a height of (h -2). The scale factor for the area is the square of the scale factor for height, so we have ...

(height ratio)^2 = 1/2

((h -2)/h)^2 = 1/2

(h -2)√2 = h . . . . . . square root; multiply by h√2

h(√2 -1) = 2√2 . . . . add 2√2 -h

h = (2√2)/(√2 -1) ≈ 6.8284 . . . units

The altitude of the original pyramid is about 6.83 units.

7 0

2 years ago

If f(x) = x² – 5, evaluate: f(x+h)-f(x)/<br> h

Likurg_2 [28]

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

<h3>How to find the derivative of a quadratic equation by definition of derivative</h3>

In this question we have a quadratic function, in which we must make use of the definition of derivative to find the expression of its first derivative. Then, the procedure is shown below:

f(x) = x² - 5 Given

f' = [(x + h)² - 5 - x² + 5] / h Definition of derivative

(x² + 2 · x · h + h² - 5 - x² + 5) / h Perfect square trinomial

(2 · x · h + h²) / h Associative, commutative and modulative properties / Existence of additive inverse

2 · x + h Distributive, commutative and associative properties / Definition of division / Existence of multiplicative inverse

2 · x h = 0 / Result

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

To learn more on derivatives: brainly.com/question/25324584

#SPJ1

6 0

2 years ago

Brown ball weighed 1.6 pounds and the green ball weighed 0.39 pounds if he placed both on the scale at the same time what will t

NemiM [27]

1.6+0.39 which is 1.99 pounds.

8 0

3 years ago

Light travels at the speed of approximately 3.0 × 108 meters per second. Find the time in minutes required for light to travel f

expeople1 [14]

Speed = distance / time => time = distance / speed
speed = 3x10^8 x 60 = 180x10^8 m per minute
time = 1.5x10^11/180x10^8 = 150x10^9/180x10^8 = 5/6x10 = 8,3 minutes

6 0

2 years ago

2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of

IgorC [24]

Answer:

a) 37.31 b) 42.70 c) 0.57 d) 0.09

Step-by-step explaanation:

We are regarding a normal distribution with a mean of 35 and a standard deviation of 6, i.e., $\mu$ = 35 and $\sigma$ = 6. We know that the probability density function for a normal distribution with a mean of $\mu$ and a standard deviation of $\sigma$ is given by

$f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]$

in this case we have

$f(x) = \frac{1}{\sqrt{2\pi}6}\exp[-\frac{(x-35)^{2}}{2(6^{2})}]$

Let $X$ be the random variable that represents a row score, we find the values we are seeking in the following way

a) we are looking for a number $x_{0}$ such that

$P(X\leq x_{0})$ = $\int\limits^{x_{0}}_{-\infty} {f(x)} \, dx = 0.65$ , this number is $x_{0}$ =37.31

you can find this answer using the R statistical programming languange and the instruction qnorm(0.65, mean = 35, sd = 6)

b) we are looking for a number $x_{1}$ such that

$P(X\leq x_{1})$ = $\int\limits^{x_{1}}_{-\infty} {f(x)} \, dx = 0.9$ , this number is $x_{1}$ =42.70

you can find this answer using the R statistical programming languange and the instruction qnorm(0.9, mean = 35, sd = 6)

c) we find this probability as

$P(28\leq X\leq 38)$ = $\int\limits^{38}_{28} {f(x)} \, dx = 0.57$

you can find this answer using the R statistical programming languange and the instruction pnorm(38, mean = 35, sd = 6) -pnorm(28, mean = 35, sd = 6)

d) we find this probability as

$P(41\leq X\leq 44)$ = $\int\limits^{44}_{41} {f(x)} \, dx = 0.09$

you can find this answer using the R statistical programming languange and the instruction pnorm(44, mean = 35, sd = 6) -pnorm(41, mean = 35, sd = 6)

6 0

3 years ago

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