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Andrej [43]
3 years ago
9

13.

Mathematics
2 answers:
RUDIKE [14]3 years ago
8 0

Answer: 2,596 cm^2

Step-by-step explanation:

Given dimensions of rectangular prism :

length: 8 cm

width: 13 cm

height: 10.5 cm

If all the dimensions of the prism are doubled, then the new dimensions will be:

length: 16 cm

width: 26 cm

height: 21 cm

The surface area of rectangular prism is given by :-

S.A.=2(lw+wh+hl)\\\\\Rightarrow\ S.A.=2(16*26+26*21+21*16)\\\\\Rightarrow\ S.A.=2,596 cm^2

Hence, its new surface area 2,596 cm^2

svetlana [45]3 years ago
7 0
The answer is 2,596 so it would be C

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What is the value of x and y?
Pavel [41]

Answer:

x=\boxed{2}

y=\boxed{4}

Step-by-step explanation:

\begin{cases} y= 6x-8... (1)\\\\y=-3x+10...(2)\end{cases}

From equations (1) & (2), we find:

6x - 8 = - 3x +10

\therefore 6x+3x = 8+10

\therefore 9x = 18

\therefore x =\frac{18}{9}

\therefore x = 2

Plug x = 2 in equation (1)

y = 6(2)-8 = 12-8 =4

So,

x=\boxed{2}

y=\boxed{4}

6 0
3 years ago
Read 2 more answers
EThe graph of a quadratic function passes through the points (6,0) and (p,0). The maximum point
MA_775_DIABLO [31]

Answer:

p = - 5

Step-by-step explanation:

The vertex of the function is (0.5, 30.25 )

Since the roots are (6, 0) and (p, 0) then the axis of symmetry is vertical

with equation x = 0.5

The axis of symmetry passes through the midpoint of the roots, thus

\frac{6+p}{2} = 0.5 ( multiply both sides by 2 )

6 + p = 1 ( subtract 6 from both sides )

p = - 5

6 0
3 years ago
WILL GIVE BRAINLIEST!!! How many terms are in the geometric sequence having a first term of 2, a last term of 32, and a common r
Elza [17]

Answer:

3

Step-by-step explanation:

first term a= 2

last term tn= 32

common ratio r= -2

number of terms

= tn=ar^n-1

32 = 2*(-2)^n-1

divide both sides by 2

32/2 = 2*(-2)^n-1/2

16 = (-2)^n-1

Then...use 16 in the power of 2

(-2)^4 = (-2)^n-1

The bases (-2), cancels out

so we have: 4 = n-1

collect like terms

4-1 = n

3 = n

n= 3

7 0
3 years ago
Solve the following ODE's: c) y* - 9y' + 18y = t^2
Nastasia [14]

Answer:

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = C_1e^{3t}+C_2e^{6t}

now calculating P.I.

P.I. = \frac{t^2}{D^2 - 9D +18}

P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

hence the complete solution

y = C.F. + P.I.

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

7 0
3 years ago
A father wishes to give his son P200, 000 ten years from now. What amount should he invest if it will earn interest at 10% compo
Archy [21]

Answer:

C. P69,256.82

Step-by-step explanation:

We know that,

The amount formula in compound interest is,

A=P(1+\frac{r_1}{n_1})^{n_1t_1} (1+\frac{r_2}{n_2})^{n_2t_2}.......

Where, P is the principal amount,

r_1, r_2.... are the annual rate for the different periods,

t_1, t_2,..... are the number of year for different periods,

n_1, n_2, n_3... are the number of periods,

Given,

A = P 200,000,

r_1=10%=0.1, n_1=4, t_1=5,r_2=12%=0.12, n_2=1, t_2=5

Thus, by the above formula the final amount would be,

200000=P(1+\frac{0.1}{4})^{4\times 5}(1+\frac{0.12}{1})^{1\times 5}

200000=P(1+0.025)^{20}(1+0.12)^5

200000=P(1.025)^{20}(1.12)^5

\implies P=69,256.824\approx 69,256.82

Option C is correct.

8 0
3 years ago
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