Simplified expression for (3x-y)(w+p-3)

Jude says that the volume of a square pyramid with base edges of 7 in and a height of 7 in is equal to the volume of a cylinder

irakobra [83]

Answer:

Jude is not correct

Step-by-step explanation:

The volume of a square pyramid is given as:

$V = a^2\frac{h}{3}$

where a = base edge and h = height

Hence, the volume of the square pyramid with base edge of 7 in and height of 7 in is:

$V = 7^2*\frac{7}{3}$

V = $114.3 in^3$ ≅ $114 in^3$

The volume of a cylinder is given as:

$V = \pi r^2h$

where r = radius and h = height

Hence, the volume of a cylinder with radius of 7 in and height of 7 in is:

$V = \pi *7^2*7$

V = $1077.57 in^3$ ≅ $1078 in^3$

Since their volumes are not equal, Jude is not correct.

8 0

4 years ago

The equation p(t) = 1.e represents a

zvonat [6]

Answer:

(b), (d) and (e)

Step-by-step explanation:

Given

$p(t) = 1 * e^t$

See attachment for $y = p(t)$

Required

Select true statements from the given options

(a) $\ln(30)$ = days the bacteria reaches 30000

We have:

$p(t) = 1 * e^t$

In this case:

$t = \ln(30)$ and $p(t) = 30000$

So, we have:

$30000 = 1 * e^{\ln(30)}$

$30000 = e^{\ln(30)}$

Using a calculator, we have:

$e^{\ln(30)} = 30$

So:

$30000 = 30$

The above equation is false.

(a) is not true

(b) The graph shows that $\ln(20) \approx 3$

We have:

$p(t) = 1 * e^t$

Let t = 3

So;

$p(3) = 1 * e^3$

From the graph, $p(3) = 20$

So:

$20 = 1 * e^3$

$20 = e^3$

Take natural logarithm of both sides

$\ln(20) = \ln(e^3)$

This gives:

$\ln(20) = 3$

(b) is true

(c) $\ln(t) = y$ is the logarithm form of $y = e^t$

We have:

$y = e^t$

Take natural logarithm of both sides

$\ln(y) = \ln(e^t)$

This gives:

$\ln(y) = t$

$\ln(y) = t$ $\ne$ $\ln(t) = y$

(c) is false

(d) $e^4 > 50$ and $\ln(50) < 4$

From the graph, we have:

$e^4 = 54$ --- rough readings

This implies that:

$e^4 > 50$ is true

Because $54 > 50$

Take natural logarithm of both sides

$\ln(54) > \ln(50)$

Rewrite as:

$\ln(50) < \ln(54)$

We have:

$e^4 = 54$

Take natural logarithm of both sides

$\ln(e^4) = \ln(54)$

$4 = \ln(54)$

$\ln(54) = 4$

Substitute $\ln(54) = 4$ in $\ln(50) < \ln(54)$

$\ln(50) < 4$

(d) is true

(e) The graph shows that $10 \approx \ln(2.3)$

We have:

$p(t) = 1 * e^t$

Let t = 2.3

So;

$p(2.3) = 1 * e^{2.3}$

From the graph,

$p(2.3) = 10$ ---- rough readings

So:

$10 = 1 * e^{2.3}$

$10 = e^{2.3}$

Take natural logarithm of both sides

$\ln(10) = \ln(e^{2.3})$

This gives:

$\ln(10) = 2.3$

(e) is true

4 0

3 years ago

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 2, 4, 8, 16

Finger [1]

<span>NOT geometric sequence. The NEGATIVE 32 breaks any initial ratio which occurs between the first four terms.<span>
</span></span>

7 0

4 years ago

An office is 20 feet long, 15 feet wide, and 12 feet high. it costs about 9 cents per year to air condition one cubic foot of sp

pentagon [3]

27$ because you do 20*15*12 then 3600*0.09 and divide that answer by 12 which is 27

7 0

3 years ago

All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that rep

prohojiy [21]

So the original price is "x".

the discounted price by 10% is P(x) = 0.9x.

the price minus a $150 coupon is C(x) = x - 150.

so, if you go to the store, the item is discounted by 10%, so you're really only getting out of your pocket 90% of that, or 0.9x, but!!! wait a minute!! you have a $150 coupon, and you can use that for the purchase, so you're really only getting out of your pocket 0.9x - 150, namely the discounted by 10% and then the saving from the coupon.

C( P(x) ) = P(x) - 150

C( P(x) ) = 0.9x - 150

5 0

4 years ago

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